Theory of plastic mechanism control for MRF–CBF dual systems and its validation

In this paper the theory of plastic mechanism control is presented for moment resisting frame–concentrically braced frames dual systems, i.e. for structural systems combined by moment resisting frames and concentrically braced frames. It is aimed at the design of structures failing in global mode, i.e. whose collapse mechanism is characterised by the yielding of all the tensile diagonals and the occurrence of buckling in the compressed ones, and by plastic hinge formation at all the beam ends and at the base of first storey columns. The proposed methodology is based on the application of the kinematic theorem of plastic collapse, by imposing that the global mechanism equilibrium curve has to lie below all the other equilibrium curves corresponding to undesired mechanisms. The practical application of the design methodology is illustrated by means of a worked example. In addition, the results of a non-linear static pushover and dynamic analyses of the designed structure are also discussed in order to demonstrate the effectiveness of the proposed design procedure.     

Seismic response of unbraced steel frames

In the analysis and design of unbraced steel frames various models are employed to represent the behaviour of beam-to-column connections. In one such model, termed here as ‘Simple Construction’, pinned connections are assumed when resisting gravity loads, whereas the same connections are assumed to be moment-resistant rigid connections when resisting lateral loads due to an earthquake or wind. Such connections are designed for moments due to lateral loads only; thus, they are not only flexible but may yield when the gravity and lateral loads act concurrently. This paper establishes the seismic performance of two (one 5-storey and the other 10-storey) unbraced steel building frames designed based on the ‘Simple Construction’ technique and on limit state principles. The first part of the paper describes briefly the design of such frames and compares their static responses with the corresponding responses of frames designed based on the ‘Continuous Construction’ assumption. Using realistic moment-rotation behaviour for flexible beam-to-column connections and realistic member behaviour, the non-linear dynamic responses of such frames for the 1940 El Centro record and 2 times the 1952 Taft record have been established using step-by-step time-history analyses. Floor lateral displacement envelopes, storey shear envelopes and cumulative inelastic rotations of beams, columns and connections are presented. The results indicate that the ‘Simple Construction’ frames experience larger lateral deflections while attracting lesser storey shears. During a major earthquake, the columns and connections of the ‘Simple Construction’ frames experience yielding, whereas in ‘Continuous Construction’ frames the beams and columns experience yielding. The cyclic plastic rotations in the connections and in the columns associated with ‘Simple Construction’ frames are found to be considerably higher.     

耗能段腹板高厚比对Y型偏心支撑钢框架滞回性能影响的试验研究

Y型偏心支撑钢框架是偏心支撑结构中抗震耗能的结构形式之一,为了研究Y型偏心支撑钢框架中耗能梁段腹板高厚比对结构滞回性能的影响,进行了2榀1/3缩尺Y型偏心支撑钢框架的低周反复荷载试验.本文主要介绍了试验过程,分析了Y型偏心支撑钢框架在循环荷载作用下的破坏机理、滞回性能、延性、刚度退化规律以及耗能能力.试验结果表明:Y型偏心支撑钢框架延性好、耗能能力强,耗能梁段腹板高厚比的改变对Y型偏心支撑钢框架强度、刚度以及耗能能力具有较大的影响.耗能梁段腹板高厚比设计得合理,Y型偏心支撑钢框架侧向刚度较大,可以满足在小震或中震作用下的结构变形要求,在大震作用下提供良好的变形能力和耗散地震能量的功能.     

自复位中心支撑钢框架结构抗震性能分析

为了研究自复位中心支撑钢框架（SC-CBF）结构的抗震性能,对一四层SC-CBF结构进行了静力弹塑性分析、低周往复加载分析和动力弹塑性时程分析,并与中心支撑钢框架（CBF）结构进行对比,探究了不同GAP单元刚度和预应力筋截面积对SC-CBF结构自复位性能及抗震性能的影响规律。结果表明:与传统CBF结构相比,SC-CBF结构的抗侧能力强,地震作用下基底剪力小,卸载后的残余变形较小,具有良好的延性性能;在极罕遇地震作用下SC-CBF结构的位移响应大,耗散的能量多,层间位移角大而残余位移小,表现出良好的自复位性能和抗震性能;GAP单元刚度对预应力筋的受力性能影响较为明显,对结构的整体受力性能和延性性能影响较小,但结构的整体受力性能和延性性能受预应力筋截面积影响显著。     

Displacement-based seismic design of hysteretic damped braces for retrofitting in-plan irregular r.c. framed structures

A displacement-based design procedure is proposed for proportioning hysteretic damped braces in order to attain, for the in-plan least seismic capacity direction and a specific level of seismic intensity, a designated performance level of a reinforced concrete (r.c.) irregular framed building to be retrofitted. To this end, a computer code for the nonlinear static analysis of spatial frames is developed to obtain the pushover curve for an assigned in-plan direction of the seismic loads. The town hall of Spilinga (Italy), a two-storey r.c. framed structure with an L-shaped plan built at the beginning of the 1960s, has been considered as case study. Four alternative structural solutions are examined, derived from the first one by the insertion of hysteretic damped braces, considering: the extended N2 and the extended pushover methods combined with a proportional and an inversely proportional in-plan stiffness distributions of hysteretic damped braces. To check the effectiveness and reliability of the design procedure, the nonlinear static response of the unbraced and damped braced frames is compared for different in-plan directions of the seismic loads. Frame members are simulated with a lumped plasticity model, including a flat surface modeling of the axial load-biaxial bending moment elastic domain, while the behavior of a hysteretic damped brace is idealized through the use of a bilinear law. Vulnerability index domains are adopted to estimate the directions of least seismic capacity at the ultimate (i.e. life-safety and collapse prevention) limit states prescribed by Italian and European seismic codes.     

Loading protocols for experimental seismic qualification of members in conventional and emerging steel frames

Quasi-static testing is one of the most commonly used experimental methods for examining the seismic performance of structural members. However, consistent loading protocols for experimental seismic qualification of members in emerging steel frames such as self-centering braced frames (SCBFs) as well as in some conventional ones including buckling-restrained braced frames (BRBFs) are still lacking. This paper aims to propose standardized loading protocols based on time-history dynamic analysis on a series of prototype building frames, including steel SCBFs, BRBFs, and moment-resisting frames (MRFs), where both far-field and near-fault earthquakes are considered. The methodology for the development of the loading protocols involves ground motion selection and scaling, design and analysis of prototype buildings, analysis results processing, and rainflow cycle counting, together with extra justification steps. The proposed loading protocols are consistently derived based on the MCE-level seismic hazard and 84^th percentile values of key seismic demand parameters. These parameters are number of damaging cycles N_t, maximum inter-story drift θ_max, inter-story drift range Δθ_i, sum of inter-story drift range ΣΔθ_i, and residual inter-story drift θ_r. The analysis confirms the variations in these seismic demands imposed on the different structural systems under different types of ground motions, highlighting the necessity of developing separate loading protocols for the different cases. The assumptions, decisions, and judgments made during the development of the loading protocols are elaborated, and the conditions and restrictions are outlined. The rationality of the proposed loading protocols is further justified through demonstrating the cumulative distribution function and energy dissipation demand of the systems.     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.     

带可替换腹板连接型耗能梁段的恢复力模型研究

带可替换耗能梁段的偏心支撑钢框架具有震后修复方便、经济等优点,但目前国内外学者对该类型的研究很少。为此,设计16组与偏心支撑钢框架采用螺栓连接的腹板连接型耗能梁段,并对16组试件进行数值模拟分析,讨论截面尺寸、耗能长度、加劲肋间距、加劲肋布置以及综合参数等变化参数对腹板连接型耗能梁段在低周往复荷载作用下的滞回性能、骨架曲线的影响,建立腹板连接型耗能梁段简化的恢复力模型。结果表明,影响腹板连接型耗能梁段耗能的主要参数是截面尺寸,建立的恢复力模型与模拟的骨架曲线对比吻合较好,可以为此类耗能梁段弹塑性分析作为参考。     

不同支撑形式高强钢组合偏心支撑抗震性能研究

耗能梁段作为偏心支撑结构的耗能元件,在大震作用下通过弹塑性变形吸收地震能量,保护主体结构处于弹性受力状态。现行规范基于强度的设计理论,为了保证耗能梁段进入塑性或破坏,梁柱构件需要进行放大内力设计,导致截面过大,而且基于强度的设计方法很难保证结构的整体破坏状态。目前,抗震设计越来越重视基于性能的设计思想,该方法能够评估结构的弹塑性反应。对于高强钢组合偏心支撑,其中耗能梁段和支撑采用Q345钢,框架梁柱采用Q460或者Q690高强度钢材,高强钢不仅带来良好的经济效益,而且能够推广高强钢在抗震设防区的应用。利用基于性能设计方法设计了4种不同形式的高强钢组合偏心支撑钢框架,包括K形、Y形、V形和D形,考虑4层、8层、12层和16层的影响。通过Pushover分析和非线性时程分析评估该结构的抗震性能,研究结果表明:4种形式的高强钢组合偏心支撑钢框架具有类似的抗震性能,在罕遇地震作用下,几乎所有耗能梁段均参与耗能,而且层间侧移与耗能梁段转角沿高度分布较为均匀。其中:D形偏心支撑具有最大的抗侧刚度,但延性较差,而Y形偏心支撑的抗侧刚度最弱,但延性最佳。     

Consolidation of inelastic clays under rectangular cyclic loading

This paper presents a semi-analytical solution for one dimensional consolidation problem of inelastic clays under cyclic loading considering the effect of the change of the consolidation coefficient of the soil layer. Due to change of the consolidation coefficient, and time-dependant loading, Terzaghi's theory would not be applicable in cyclic conditions. In this research, a method based on the time variable exchange along with the superimposing rule is employed to overcome these shortcomings. Changes in the consolidation coefficient are applied in the solution by modifying the loading and unloading durations introducing a Virtual Time. Based on the superimposing rule a set of continuous static loads in specified times are used instead of the cyclic load in the transformed time space. Each full cycle of loading is replaced by a pair of static loads with different signs. Based on the Terzaghi's theory the pore-water pressure distribution and the degree of consolidation are calculated for each static load and the results are superimposed. A set of laboratory consolidation tests under cyclic load and numerical analysis are performed in order to verify the presented method. The numerical solution and laboratory tests results showed the accuracy of the presented method.     

Response spectrum techniques for three-component earthquake design

An evaluation is made of response spectrum techniques as applied to seismic analysis and design of steel template offshore platforms. Such structures are designed as braced space frames for several loading conditions, including the simultaneous action of three earthquake components. Base shears as well as gross forces and combined stresses in members of three different platforms are computed for 30 real, three-component earthquakes and response spectrum predictions, obtained by several modal-spatial combination methods, are compared to time history solutions. Results are presented in the form of error statistics. The three approximations examined are: (a) combination of modes for one component input, (b) combination of the three partial responses to obtain estimates of total response and (c) combination of gross forces to derive maximum design stresses at a section. Attention is focused on corner piles because these are among the most heavily penalized members by three-component excitations. It is shown that commonly used spatial combination rules may underestimate gross forces in design controlling corner members by 15–30 per cent on the average. This is attributed to correlations between motion components that create additive effects along certain directions. Typical estimates of combined stresses, however, are found to be slightly conservative.     

Development and subassemblage cyclic testing of hybrid buckling-restrained steel braces

Buckling-restrained braced frames (BRBFs) are vulnerable to relatively higher post-earthquake residual drifts under high intensity ground shakings. This is primarily due to the low axial elastic and post-elastic stiffness of buckling-restrained braces (BRBs) satisfying the design force demand requirements. In the present study, a hybrid buckling restrained bracing system consisting of a short yielding core length BRB component and a conventional buckling-type brace component connected in series has been developed with an aim to increase the axial stiffness of braces. This study is focused on the experimental investigation of six hybrid bucking restrained braces (HBRBs) to investigate their overall behavior, load-resisting capacity, strength-adjustment factors and energy dissipation potential. The main parameters varied are the cross-sectional area, the yielding length of core elements as well as the detailing of buckling-restraining system of short yielding core length BRBs. Test results showed that the HBRBs with yielding core length in the range of 30% of work-point to work-point lengths withstood an axial strain of 6% without any instability and can deliver stable and balanced hysteretic response and excellent energy dissipation under reversed cyclic loading conditions.

     

Hybrid simulation of a zipper‐braced steel frame under earthquake excitation

Hybrid simulation is a testing methodology that combines laboratory and analytical simulation to evaluate seismic response of complex structural framing systems. One or more portions of the structure, which may be difficult to model numerically or have properties that have not been examined before, are tested in one or more laboratories, whereas the remainder of the structure is modeled in software using one or more computers. These separate portions are assembled such that combined dynamic response of the hybrid model to excitation is computed using a time‐stepping procedure. A hybrid simulation conducted to examine the seismic response of a type of steel concentrically braced frame, the suspended‐zipper‐braced frame, is presented. The hybrid simulation testing architecture, hybrid model, test setup, solution algorithm, and the seismic response of the suspended‐zipper‐braced frame hybrid model are discussed. Accuracy of this hybrid simulation is examined by comparing hybrid and computer‐only simulations and the errors are quantified using an energy‐based approach. This comparison indicates that the deployed hybrid simulation method can be used to accurately model the seismic response of a complex structural system such as the zipper‐braced frame. Copyright © 2008 John Wiley & Sons, Ltd.     

Concentrically braced steel frames under seismic actions: Non-linear behaviour and design coefficients

The paper deals with the non-linear dynamic analysis of concentrically braced pinned frames under earthquake conditions. A model is first presented for the behaviour of bars subjected to cyclic axial force, which takes into account the overall and local buckling phenomena, section shape, residual stresses, material behaviour and damage accumulation due to low-cycle fatigue and fracture. Dynamic analyses of bracing systems are then described: these have been performed, on the basis of the axially loaded bar model, within the framework of a simplified procedure for the determination of optimal design factors. The results obtained are first reported for the case of one-storey systems; an example of the behaviour of a four-storey system is given finally.     

Influence of gusset plate connections and braces on the seismic performance of X‐braced frames

Braced frames are one of the most economical and efficient seismic resisting systems yet few full‐scale tests exist. A recent research project, funded by the National Science Foundation (NSF), seeks to fill this gap by developing high‐resolution data of improved seismic resisting braced frame systems. As part of this study, three full‐scale, two‐story concentrically braced frames in the multi‐story X‐braced configuration were tested. The experiments examined all levels of system performance, up to and including fracture of multiple braces in the frame. Although the past research suggests very limited ductility of SCBFs with HSS rectangular tubes for braces recent one‐story tests with improved gusset plate designs suggest otherwise. The frame designs used AISC SCBF standards and two of these frames designs also employed new concepts developed for gusset plate connection design. Two specimens employed HSS rectangular tubes for bracing, and the third specimen had wide flange braces. Two specimens had rectangular gusset plates and the third had tapered gusset plates. The HSS tubes achieved multiple cycles at maximum story drift ratios greater than 2% before brace fracture with the improved connection design methods. Frames with wide flange braces achieved multiple cycles at maximum story drift greater than 2.5% before brace fracture. Inelastic deformation was distributed between the two stories with the multi‐story X‐brace configuration and top story loading. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.     

消能支撑框架结构的非线性分析

本文介绍了六榀钢筋混凝土支撑框架模型（两榀为普通支撑框架，另四榀为消能支撑框架）在低周反复荷载作用下的工作性能和试验结果；编制了非线性程序，对试验模型进行了计算分析，计算结果和试验实测值符合较好；另外还计算了两榀足尺消能支撑框架结构，研究不同的消能器滑移荷载对结构抗震能力的影响，结果表明消能支撑框架结构具有良好、稳定的抗震性能。     

Fuzzy optimum design of aseismic structures

It was pointed out in our previous paper that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures. Then the idea of fuzzy optimum design of structures was first proposed and the problem with fuzzy allowable intervals of the physical variables (structural responses and sizes) could be solved via the α-level cut approach. In this paper, the procedure of fuzzy optimum design of aseismic structures is further developed. For this purpose, the concepts and definitions of fuzzy predictive earthquake intensity, fuzzy response spectrum and fuzzy structural response are given. A solution of the programming problems with generalized fuzzy constraints (including both fuzzy constraint functions and their fuzzy allowable intervals) is put forward; one of its special cases is the χ-level cut solution in Reference 1. The satisfaction degree of a fuzzy constraint function to its fuzzy allowable interval is defined, by which the problem considered is transformed into a series of non-fuzzy programmings. Then, a series of optimum points can be obtained which make up the solution of the fuzzy programming. As the solution of fuzzy programming contains not one but a series of optimum points, a two-step approach is presented to the fuzzy optimum design of aseismic structures. The first step is to find out the set of minimum cost design points corresponding to different design levels. In the second step, both construction cost and earthquake-caused loss expectation in the service life of the structure are traded off to find the optimum design level as well as a corresponding optimum design scheme.     

A design procedure for suspended zipper‐braced frames in the framework of Eurocode 8

In the recent past, suspended zipper‐braced frames were proposed to avoid one‐storey collapse mechanisms and dynamic instability under severe ground motions. In this paper, the design procedure suggested by Yang et al. is first slightly modified to conform to the design approach and capacity design rules stipulated in Eurocode 8 for concentrically braced frames. The procedure is applied to a set of suspended zipper‐braced frames with different number of storeys and founded on either soft or rock soil. The structural response of these frames is analysed to highlight qualities and deficiencies and to assess the critics reported by other researchers with regard to the design procedure by Yang et al. Then, improvements are proposed to this procedure to enhance the energy dissipation of the chevron braces and the response of the structural system as well. The effectiveness of the design proposals is evaluated by incremental dynamic analysis on structures with different geometric properties, gravity loads and soil of foundation. Copyright © 2017 John Wiley & Sons, Ltd.